On novel Hamiltonian description of the nonholonomic Suslov problem

2025/05/26 by Tsiganov, A. V. · 1 citation
#Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2505.19594

Abstract

We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets on the five dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in these cases.

Citations

• Homogeneous potentials, Lagrange's identity and Poisson geometry
• On tensor invariants of the Clebsch system
• Multisymplectic structure of nonintegrable Henon-Heiles system
• On tensor invariants for integrable cases of Euler, Lagrange and Kovalevskaya rigid body motion
• Almost-Poisson brackets for nonholonomic systems with gyroscopic terms and Hamiltonisation

Cited by

• Homogeneous potentials, Lagrange's identity and Poisson geometry

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